Not necessarily. It's easier in Lisp, and a decades-long tradition, but Lisp is not even the only language of which that's true—there's also Forth. And there are many opportunities to apply this approach beyond those two. The more the better, because each qualitatively different starting point will lead to qualitatively different systems.

The software ecosystem is not well served by everyone being focused on the same few familiar programming approaches. Sure there are economies of scale—better tooling, programmer fungibility—but there is less intellectual diversity. More people should realize the tradeoffs here: yes you lose a lot when you start making your own language, but you also gain a lot. The program you're trying to write becomes more writeable. If that doesn't sound significant, it's because we're so conditioned to think the other way. There's another advantage, too: it's deeply intellectually rewarding. That provides staying power to work on significant projects over the long haul and is a solid motivation to do something many people think is crazy.

Or OMeta http://tinlizzie.org/ometa/ or Ohm https://github.com/harc/ohm or the like